Maciej Dolęga ; Piotr Sniady - Polynomial functions on Young diagrams arising from bipartite graphs

dmtcs:2908 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2908
Polynomial functions on Young diagrams arising from bipartite graphs

Authors: Maciej Dolęga 1; Piotr Sniady 2

  • 1 Instytut Matematyczny
  • 2 Instytut Matematyczny PAN

We study the class of functions on the set of (generalized) Young diagrams arising as the number of embeddings of bipartite graphs. We give a criterion for checking when such a function is a polynomial function on Young diagrams (in the sense of Kerov and Olshanski) in terms of combinatorial properties of the corresponding bipartite graphs. Our method involves development of a differential calculus of functions on the set of generalized Young diagrams.

https://doi.org/10.46298/dmtcs.2908
Source: HAL:hal-01215109v1
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Polynomial functions on Young diagrams,coloring of bipartite graphs,differential calculus on Young diagrams,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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Source : ScholeXplorer IsRelatedTo ARXIV math/9712267
Source : ScholeXplorer IsRelatedTo DOI 10.1007/bf02467066
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/9712267
  • 10.1007/bf02467066
  • 10.1007/bf02467066
  • math/9712267
  • 10.48550/arxiv.math/9712267
Anisotropic young diagrams and jack symmetric functions

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